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Here is the data on all .750 (win%) teams that didnt make the playoffs for one reason or another since 1934. Only 9 of the 15 were bumped by division winners. You might note the most significant casualty was the 1967 Colts that got bumped by the Lomabardi Packers. Thus if we change the system too much perhaps we should also discuss whose name should even be on the trophy.
I would rather just take the 4 division winners and get rid of the wild card altogether.
Bumped by Division Winner 1 1934Lions 10-3 Giants 8-5 2 1936Bears 9-3 Redskins 7-5 3 1939Redskins 8-2-1 n/a 4 1942Packers 8-2-1 n/a 5 1943Packers 7-2-1 Redskins/Giants 6-3-1 6 1944Eagles 7-1-2 n/a 7 1948Bears 10-2 Eagles 9-2-1 8 1951Giants 9-2-1 Rams 8-4 9 195349ers 9-3 n/a 10 1956Lions 9-3 Giants 8-3-1 11 1962Lions 11-3 n/a 12 1963Packers 11-2-1 Giants 11-3 13 1964Cardinals 9-3-2 n/a 14 1967Colts 11-1-2 Browns/Packers/Cowboys 9-5/9-4-1 15 1968Rams 10-3-1 Browns/Vikings 10-4/8-6
.750 is not the proper percentage to use for this exercise. That's a 12-4 record in today's game, so this data is not surprising - A 12-4 team missing the playoffs literally has never happened, especially after the institution of Wild Card teams in 1970 (and the advent of the 16-game season in 1978). So once again, no surprise that the cut off of your data is 1968.
The proper percentages to use for this data analysis would be <= .625 (10-6) or .5625 (9-7) versus >= .5625 (9-7) or .500 (8-8).